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AP = CQ and RPBQ is cyclic; prove that RX = RY

Source: All-Russian Olympiad 2006 finals, problem 9.6

May 7, 2006
geometrycircumcirclegeometry proposed

Problem Statement

Let PP, QQ, RR be points on the sides ABAB, BCBC, CACA of a triangle ABCABC such that AP=CQAP=CQ and the quadrilateral RPBQRPBQ is cyclic. The tangents to the circumcircle of triangle ABCABC at the points CC and AA intersect the lines RQRQ and RPRP at the points XX and YY, respectively. Prove that RX=RYRX=RY.
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